Related papers: An abstract $L^2$ Fourier restriction theorem

We investigate the boundedness of oscillating singular integrals on Lie groups of polynomial growth in order to extend the classical oscillating conditions due to Fefferman and Stein for the boundedness of oscillating convolution operators.…

By using the notion of contraction of Lie groups, we transfer $L^p-L^2$ estimates for joint spectral projectors from the unit complex sphere $\sfera$ in ${{\mathbb{C}}}^{n+1}$ to the reduced Heisenberg group $h^{n}$. In particular, we…

We present a quick approach to computing the $K$-theory of the category of locally compact modules over any order in a semisimple $\mathbb{Q}$-algebra. We obtain the $K$-theory by first quotienting out the compact modules and subsequently…

We investigate conditions for the extendibility of continuous algebra homomorphisms $\phi$ from the Fourier algebra $A(F)$ of a locally compact group $F$ to the Fourier-Stieltjes algebra $B(G)$ of a locally compact group $G$ to maps between…

We find equivalent conditions determining the representation type of abelian restricted Lie algebras in terms of how their Green ring of restricted representations varies with respect to different cocommutative Hopf algebra structures on…

Let $A/K$ be an abelian variety with real multiplication defined over a $p$-adic field $K$ with $p>2$. We show that $A/K$ must have either potentially good or potentially totally toric reduction. In the former case we give formulas of the…

In this paper, we classify the possible group structures on the set of $R$-valued points of an abelian variety, where $R$ is any real closed field. We make use of a family of abelian varieties that, in effect, allows one to quantify over…

We introduce a notion of $L^2$-Betti numbers for locally compact, second countable, unimodular groups. We study the relation to the standard notion of $L^2$-Betti numbers of countable discrete groups for lattices. In this way, several new…

The Fourier transform, known in classical analysis, and generalized in abstract harmonic analysis, can also be considered in the theory of locally compact quantum groups. In this note, I discuss some aspects of this more general Fourier…

In this paper, we construct a large class of new simple modules over the twisted $N=2$ superconformal algebra. These new simple modules are restricted modules based on the simple modules over certain finite-dimensional solvable Lie…

In this paper we study the category LCA(2) of certain non-locally compact abelian topological groups, and extend the notion of Weil index. As applications we deduce some product formulas for curves over local fields and arithmetic surfaces.

In this paper, we study the $L^{2}$-boundedness and $L^{2}$-compactness of a class of $h$-Fourier integral operators. These operators are bounded (respectively compact) if the weight of the amplitude is bounded (respectively tends to $0)$.

We consider several questions about restriction of representations of classical and metaplectic groups over local and global fields to subgroups, extending considerably the scope of the earlier work on $SO(n),SO(n-1)$. This includes Bessel…

We establish regularity conditions for $L_p$-boundedness of Fourier multipliers on the group von Neumann algebras of higher rank simple Lie groups. This provides a natural H\"ormander-Mikhlin criterion in terms of Lie derivatives of the…

These notes briefly discuss basic notions concerning locally compact abelian topological groups and Fourier transforms of functions on them.

In this short note we first extend the validity of the spectral radius formula obtained in \cite{ag} to Fourier--Stieltjes algebras. The second part is devoted to showing that for the measure algebra on any locally compact non-discrete…

In this note we study two related questions. (1) For a compact group G, what are the ranges of the convolution maps on A(GXG) given for u,v in A(G) by $u X v |-> u*v' ($v'(s)=v(s^{-1})$) and $u X v |-> u*v$? (2) For a locally compact group…

We continue our research on Fourier restriction for hyperbolic surfaces, by studying local perturbations of the hyperbolic paraboloid $z=xy$ which are of the form $z=xy+h(y),$ where $h(y)$ is a smooth function which is flat at the origin.…

We study irreducible restrictions from modules over alternating groups to subgroups. We get reduction results which substantially restrict the classes of subgroups and modules for which this is possible. This is known when the…

A locally compact group $ G $ is discrete if and only if the Fourier algebra $ A(G) $ has a non-zero (weakly) compact multiplier. We partially extend this result to the setting of ultraspherical hypergroups. Let $H$ be an ultraspherical…